Optic fibres are used to guide light over meters to many kilometers. They work by confining the light to a central core. Examples of known structures for optic fibres are briefly described below.
In the commonly used single mode optic fibre, the core that carries the light is surrounded by a layer of cladding, as may be seen in FIG. 1a. Both the core and cladding are typically glass but the core is made of a high refractive index material whilst the cladding has a lower refractive index, so that light in the core undergoes total internal reflection at the interface between the two layers and so is confined to the core. FIG. 1b is an example of the refractive index variation.
In recent years, photonic waveguiding structures have been proposed, such as the so-called “OmniGuide” fibre (see FIG. 2), which has been described at M. Ibanescu et al, Physical Review E, Vol. 67(4), article number 046608, 2003. In this, alternate concentric layers of high and low refractive index surround a core, the structure being periodic in the radius. The periodicity acts as a bandgap to exclude certain wavelengths and thus confine them to the core.
Another proposal has been to radially grade the refractive index from a high value at the centre of the fibre to a low value. This serves to refract the light rays at the boundary between each layer (which can be considered infinitesimally thin if the refractive index variation is continuous). This serves to bend rays on trajectories away from the axis of the fibre back towards that axis. A graded index or “GRIN” fibre is illustrated in FIG. 3a. Typically, the refractive index variation is parabolic as shown in FIG. 3b. 
Another problem that has been under consideration in the area of photonics is the coupling of light between waveguides of different width. Single mode glass optic fibres and also polymer waveguides have relatively low refractive index, making the core width relatively large (to obtain the single mode operation), whereas silicon waveguides (silicon being used because photonic devices are often manufactured in silicon) have a relatively high refractive index, and so have a relatively small waveguide width. There is, therefore, a difficulty in efficiently transferring light from optic fibres and polymer waveguides into silicon waveguides.
FIG. 4 shows one proposal to overcome this. Instead of simply abutting the end of, in this example a polymer waveguide to the end of a silicon waveguide, a tapered section of the silicon waveguide is extended into the polymer core over some distance. The taper collects more of the light from the polymer core and transmits it into the silicon core. The device is further described at T Shoji et al, 15th LEOS Conf. Proc., Vol. 1, TuU3, p289–290, 2002.
Another proposal is to use a short section of graded index fibre as a lens to concentrate light from the wide exit aperture of the fibre or polymer waveguide into the smaller aperture at the end of the silicon waveguide. The action of such a lens is illustrated in FIG. 5, which shows the rays from the wide glass optic fibre aperture being converged by the index variation to a focus, which is where the input aperture to the silicon waveguide is placed.